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Using a modified version of the 1½-D BALDUR transport code, important aspects of the time evolution of D-T plasmas in a compact, high field tokamak of the Ignitor type with strong Ohmic heating are investigated. For the canonical electron heat transport, a generalization of the Coppi-Mazzucato-Gruber diffusion for axisymmetric toroidal geometry is assumed as well as alpha particle heating contributions; this reproduces the power dependent degradation of confinement observed in present-day auxiliary heated experiments. Anomalous ion heat conductivity is based on the existence of the ηi mode halfway out in the discharge, with an assumed spatial dependence of the transport magnitude superimposed on a parameter scaling related to wave breaking in the direction perpendicular to the magnetic field. The particle density profiles are held fixed, and convective energy fluxes are ignored. Results from three model examples associated with the set of transport coefficients are considered, and the impact of variations in density, conductivity magnitudes, resistivity, plasma impurity level and flux surface equilibrium configuration on the approach to ignition is discussed.